How to solve sudoku

A sudoku is a 9 by 9 grid split into nine 3 by 3 boxes. Fill it so that every row, every column and every box contains the digits 1 to 9 exactly once. A well-made puzzle has one solution, and you can always reach it by logic. You never need to guess.

1. Scan for the easy cells

Start with the digit that already appears most often. Take a 5, for example. Every 5 already on the grid rules out the rest of its row, column and box. Look at a box that has no 5 yet: if the 5s elsewhere block all but one of its empty cells, the 5 goes there. This is the hidden single, found by scanning. Repeat with every digit, and go round again whenever you place something, because each new digit blocks more cells.

Also look for rows, columns and boxes with only one empty cell left. The missing digit is forced: that is a full house.

2. Write the candidates

When scanning stops giving results, write down, in each empty cell, the digits that could still go there. These are the candidates or pencil marks. The app can show them for you. A cell with only one candidate left must take it: a naked single. Cross out the digit you place from the candidates of every cell in its row, column and box, and look again.

3. Pairs and locked candidates

Now look at what the candidates tell you together. If two cells in a row hold only the same two candidates, those two digits belong to those cells, and nowhere else in that row can have them: a naked pair. If a digit can only go in two cells of a unit, and another digit too, and no other digits fit there, you have a hidden pair. If, inside a box, a digit can only go in one row, then it cannot appear anywhere else in that row: locked candidates. These steps remove candidates, and the removals often unlock new singles.

4. Patterns across the grid

Harder puzzles need a pattern that connects cells far apart. Learn them in this order, since each builds on the one before:

• X-Wing and Swordfish: a digit confined to the same columns in two or three rows.
• Skyscraper, Two-String Kite and Empty Rectangle: single-digit patterns made of two strong links.
• XY-Wing, XYZ-Wing and W-Wing: cells with two or three candidates that force a digit between them.
• Simple Colors and X-Chains: following the links of a single digit.

The technique index lists all of them, with an example board for each.

If you are stuck

A puzzle that seems to offer nothing usually has a step you have not looked for yet, not a guess waiting to be made. Open the solver and ask for a hint: it names the technique and shows the cells involved, and the guide for that technique explains why it works. Then try the next one yourself before asking again.